Bibtex

publisher = "Department of Mathematics, Technical University of Denmark",

author = "Ilkka Holopainen and Steen Markvorsen and Vicente Palmer",

year = "2006",

series = "Mat-Report",

}

RIS

TY - RPRT

T1 - p-Transience and p-Hyperbolicity of Submanifolds

A1 - Holopainen,Ilkka

A1 - Markvorsen,Steen

A1 - Palmer,Vicente

AU - Holopainen,Ilkka

AU - Markvorsen,Steen

AU - Palmer,Vicente

PB - Department of Mathematics, Technical University of Denmark

PY - 2006

Y1 - 2006

N2 - We use drifted Brownian motion in warped product
model spaces as comparison constructions to show
$p$-hyperbolicity of a large class of submanifolds
for $p\ge 2$.
The condition for $p$-hyperbolicity is expressed in
terms of upper support functions for the radial
sectional curvatures of the ambient space and for
the radial convexity of the submanifold. In the
process of showing $p$-hyperbolicity we also obtain
explicit lower bounds on the $p$-capacity of
finite annular domains of the submanifolds in
terms of the drifted $2$-capacity of the
corresponding annuli in the respective comparison
spaces.

AB - We use drifted Brownian motion in warped product
model spaces as comparison constructions to show
$p$-hyperbolicity of a large class of submanifolds
for $p\ge 2$.
The condition for $p$-hyperbolicity is expressed in
terms of upper support functions for the radial
sectional curvatures of the ambient space and for
the radial convexity of the submanifold. In the
process of showing $p$-hyperbolicity we also obtain
explicit lower bounds on the $p$-capacity of
finite annular domains of the submanifolds in
terms of the drifted $2$-capacity of the
corresponding annuli in the respective comparison
spaces.